Answer:
a). ![V=\frac{U.F}{U-F}](https://tex.z-dn.net/?f=V%3D%5Cfrac%7BU.F%7D%7BU-F%7D)
b). V = 15 units
Step-by-step explanation:
Focal length F of a lens made by combining two lenses of different focal lengths U and V will be,
![\frac{1}{F}=\frac{1}{U}+\frac{1}{V}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7BF%7D%3D%5Cfrac%7B1%7D%7BU%7D%2B%5Cfrac%7B1%7D%7BV%7D)
A). By solving the given formula,
![\frac{1}{V}=\frac{1}{F}-\frac{1}{U}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7BV%7D%3D%5Cfrac%7B1%7D%7BF%7D-%5Cfrac%7B1%7D%7BU%7D)
![\frac{1}{V}=\frac{U-F}{U.F}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7BV%7D%3D%5Cfrac%7BU-F%7D%7BU.F%7D)
![V=\frac{U.F}{U-F}](https://tex.z-dn.net/?f=V%3D%5Cfrac%7BU.F%7D%7BU-F%7D)
B). If F = 6 and U = 10 then we have to find the value of V.
By substituting the given values in the formula,
![V=\frac{6\times 10}{10-6}](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B6%5Ctimes%2010%7D%7B10-6%7D)
![V=\frac{60}{4}](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B60%7D%7B4%7D)
V = 15 units
Therefore, focal length (V) of the lens = 15 units
GCF means the term(s) that 6x and x have.
The GCF is x because:
1. Using multiplication: 6x * x = 6x^2
becomes x(6+x) = 6x^2
GCF is x.
Good luck to you!
Sample space = {6 cookies and 9 peanuts} = 15
1st draw :P(1 cookie) = 6/15
2nd draw P(also 1 cookie) = 5/14
3rd draw P(also 1 cookie) = 4/13
total probability = 6/15 x 5/14 x 4/13 = 4/91
Answer:
10.4%
Step-by-step explanation:
![\$47 \:to \: \$42.13\\\\47 - 42.13\\\\= \$4.87\\\\= \frac{4.87}{47} \times 100\\\\\frac{487}{47} \\\\=10.36 \\= 10.4 \%](https://tex.z-dn.net/?f=%5C%2447%20%5C%3Ato%20%5C%3A%20%20%5C%2442.13%5C%5C%5C%5C47%20-%2042.13%5C%5C%5C%5C%3D%20%5C%244.87%5C%5C%5C%5C%3D%20%5Cfrac%7B4.87%7D%7B47%7D%20%20%5Ctimes%20100%5C%5C%5C%5C%5Cfrac%7B487%7D%7B47%7D%20%5C%5C%5C%5C%3D10.36%20%5C%5C%3D%2010.4%20%5C%25)